Equation 677 Database

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Magma 08344ab42a12…

magma 08344ab42a12
Size
595
Isomorphism class hash
08344ab42a120301898a60fd3d84e7630026af31e93b727d455e79f8fbed01bf
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 594) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-08 18:22:58
Display reorder
133,132,134,135,136,137,317,316,315,320,318,319,332,334,333,330,331,329,385,384,386,383,381,382,400,399,401,404,402,403,510,515,512,517,564,283,285,286,287,282,284,257,256,252,253,254,255,185,184,180,181,182,183,113,112,108,109,110,111,227,226,222,223,224,225,57,56,58,59,54,55,10,9,11,6,7,8,157,156,158,159,160,161,239,238,234,235,236,237,167,166,162,163,164,165,323,322,324,325,326,327,407,406,405,409,410,408,336,335,337,339,340,338,360,359,361,364,362,363,481,480,508,507,478,479,321,461,425,463,426,462,534,533,527,524,532,525,582,550,587,567,566,568,574,570,584,592,19,21,22,23,18,20,95,94,90,91,92,93,29,28,24,25,26,27,169,168,170,171,172,173,139,138,140,141,142,143,207,206,208,209,204,205,86,85,87,88,89,84,51,50,52,49,48,53,120,125,121,122,123,124,16,15,17,12,13,14,432,431,328,466,500,465,491,501,492,490,488,489,509,487,499,486,454,453,464,429,430,428,427,443,309,311,310,307,308,306,365,469,434,468,433,467,542,535,541,514,540,520,573,579,557,556,555,571,547,546,561,559,186,188,189,190,191,187,67,66,68,69,70,71,60,65,61,62,63,64,267,266,268,269,264,265,291,290,292,293,288,289,32,31,33,34,35,30,198,203,199,200,201,202,217,216,218,219,220,221,39,38,40,41,36,37,83,82,78,79,80,81,344,346,345,343,341,342,376,375,377,378,379,380,370,369,368,373,371,372,348,347,349,352,350,351,475,474,506,374,505,473,472,367,471,504,470,366,536,537,513,522,521,529,593,569,552,578,581,589,551,554,548,575,174,176,177,178,179,175,296,295,297,298,299,294,258,263,259,260,261,262,149,148,144,145,146,147,128,127,129,130,131,126,276,281,277,278,279,280,195,194,196,197,192,193,212,211,213,214,215,210,77,76,72,73,74,75,154,153,155,150,151,152,460,424,423,314,312,313,397,396,398,393,394,395,412,414,413,415,416,442,450,484,417,485,451,452,389,388,387,390,391,392,422,420,502,498,503,421,531,543,511,519,518,526,563,591,594,577,580,565,588,576,553,572,275,271,272,273,274,270,241,240,242,243,244,245,247,246,248,249,250,251,106,105,107,102,103,104,101,100,96,97,98,99,305,304,300,301,302,303,116,115,117,118,119,114,230,229,231,232,233,228,46,45,47,42,43,44,1,5,0,2,3,4,477,438,437,435,436,476,493,456,455,419,459,497,447,449,448,444,445,446,439,482,411,483,440,441,353,355,354,357,358,356,418,496,458,494,457,495,539,538,530,516,523,528,558,544,585,560,583,562,586,545,549,590 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 595 = 35 + 5*112, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 5, B) with E = magma#967d317cf04778fc566aed88226f2ec73cf112a27da243deb50eb6f078cd5ea3, M = the submagma generated by {30, 84} (35 elements) in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(5, 112): MacNeish's product over GF(16) x GF(7); GF(16) = F_2[x]/(x^4 + x + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 85.

last edited by qawbecrdtey at 2026-10-08 18:22:59 · history